It is known that computing $a^x \bmod N$ takes $O(|x| + \mathrm{pop}(x))$ multiplications modulo $N$, where $|x|$ is the number of bits of $x$ and $\mathrm{pop}(x)$ is the number of $1$ bits (Hamming ...

According to this document the padded message has the following structure:
$EM \;= \; 0x00 \; || \; 0x02 \; || \; PS \; || \; 0x00 \; || \; M$
What is the purpose of this null byte at the beginning ...

I'm trying to prove something and if I can show that there is a simple way to calculate $(g^a \bmod p)^k$ if I know both $g^k \bmod p$ and $g^a \bmod p$, then (I think) it will help me prove it, but ...

I can calculate $Q = a\,b\,G$ in several ways:
$Q = a \, (b \, G)$ or $Q = b \, (a \, G)$. These give the same result, as expected.
But if I do $c = (a \, b) \bmod n$ where $a \, b$ is much greater ...

I'm currently working on Ciphertext Policy Attribute-Based Encryption (CP-ABE). So far I'm only using it with a basic understanding how it actually works. Now I want to understand it a bit better, but ...

How to compute $ g^{1/(e_1+s)}$, where $g$ is the generator of group $\mathbb G$, and $e_1$ and $s$ are keys? I know only $s$ and $g^{e_1}$, not $e_1$. $\mathbb G$ has prime order for some prime $p$ ...

Is there any function $f : \mathbb{Z}_n \rightarrow \mathbb{Z}^\times_n$ that is invertible?
By invertible, I mean it given $y \in \mathbb{Z}^\times_n$, it should be easy to find $x \in \mathbb{Z}_n$ ...